This problem is from the Columbus State University problem of the week. Link

### Problem

Given , find the value of .

### Solution

Note that this string of equalities gives us the following relations.

We will first solve for which will in turn allow us to solve for the other values. Equations (1), (2), and (3) tell us that , , and , respectively. If we substitute these values into equation (4) we find

Thus we can use equations (1), (2), and (3) to find that , , and . Their sum is

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Another way to solve this problem is using linear algebra. Note that the string of equalities gives us the following relations:

This allows us to set up two matrices:

and

Then when you compute

you find .